Did I mess up going no contact

Got dumped by gf of 2 years roughly a couple months ago. She said she wanted to try with me again eventually but just needed time as she wasn’t in a good state to be a gf. We stayed in contact for a while but I decided to go no contact with her to try to heal as I was unsure of whether or not she was serious about getting back with me. In retrospect, I think she was. I tried to reach out and rekindle with her but she’s already seeing someone else and doesn’t see anything with me. Did I ruin our chances of getting back together by forcing no contact? Our relationship was generally fine, none of us did anything bad, so it sucks.